\>But additionally I need to manage and install some external dependencies that are likely to be somewhat annoying. Specifically I need to add the PostgreSQL installer to this

MSIX package installation supports MSIX package dependencies, and a very limited set of not-MSIX dependencies (notably, WebView2 via <win32dependencies:ExternalDependency>. MSIX has no support to 'chain installers' to e.g. automagically run PostgresSQL's installer when installing your MSIX package.

Does PostgresSQL offer installation as MSIX package(s)?

Alternatively, you might consider winget to install your package and PostgresSQL.